Q: Is there a shape that has no line of symmetry but has the rotational symnetry of 4?

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Yes. Any equilateral shape can have both rotational and line symmetry.

A semicircle.

A line segment would have rotational symmetry.

The letters S, N, Z, for example.

A triangle........I think

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Yes. Any equilateral shape can have both rotational and line symmetry.

A semicircle.

circle

A line segment would have rotational symmetry.

Yes, it is possible to have a shape that has a line of symmetry but does not have rotational symmetry. An example is the letter "K", which has a vertical line of symmetry but cannot be rotated to match its original orientation.

How about an isosceles trapezoid

The letters S, N, Z, for example.

A triangle........I think

Parrallelogram (it has rotational symmetry but no lines of symmetry)

The letters H and Z have both line symmetry and rotational symmetry

A shape does NOT need to have line symmetry in order to have rotational symmetry.For example, the letters N, Z and S can be rotated 180° to show symmetry, but none of these show line symmetry.When the folded part Line of Symmetry. Here I have folded a rectangle one way, and it didn't work.

It has line symmetry (straight down the center) but not rotational symmetry.